The number of solutions of the equation `cos6x+tan^2x+cos6xtan^2x=1` in the interval `[0,2pi]` is 4 (b) 5 (c) 6 (d) 7

Options

A. 4
B. 5
C. 6
D. 7

Answer

D

Explanation

`cos 6x=(1-tan^(2) x)/(1+tan^(2) x) = cos 2x`
`rArr 2 sin 2x. Sin 4x =0`
`rArr sin x. cos x. sin 4x=0`
`rArr x=n pi, 4pi = m pi, m, n in Z`
`rArr x=n pi, x=(mpi)/4, m, n in Z`
`:. x=0, pi/4, (3pi)/4, pi, (5pi)/4, (7pi)/4, 2pi`